My guess is when the toilet was replaced, the wax roap seal around the base was not installed properly, and is allowing septic gas out. The wax seal must provide an air-tight seal around the sewer flange. If its water-tight but nut air-tight, you will smell shit. In my house, the flange was too low and I could not get a good seal. Had to raise the flange, then reseal and mount the toilet. Anyway, that's my guess.